1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Sladkaya [172]
3 years ago
5

Prove: Let x and y be positive real numbers. If x ≤ y, then √x ≤ √y.

Mathematics
1 answer:
shutvik [7]3 years ago
7 0

Suppose that x,y> 0 and that x\leq y. We can subtract x from both sides to obtain y-x \geq 0. Recall that (a+b)(a-b)=a^2-b^2. Now we can replace a and b in this identity with \sqrt{y} and \sqrt{x} respectively and we get (\sqrt{y}-\sqrt{x})(\sqrt{y}+\sqrt{x})=y-x. From this it follows that (\sqrt{y}-\sqrt{x})(\sqrt{y}+\sqrt{x}) \geq 0. Since \sqrt{y}+\sqrt{x} > 0, we can divide by it both sides of the inequality without altering its direction and end up with \sqrt{y}-\sqrt{x} \geq 0. Now we just need to add \sqrt{x} to both sides and conclude that \sqrt{y} \geq \sqrt{x}, which finishes our proof.

You might be interested in
The product of x and 6 is at least -17
mr_godi [17]

The product of x and 6: 6(x)

is at least -17: ≥ 17

6x ≥ 17 is your answer

hope this helps

7 0
3 years ago
Joel needs to buy some blank DVDS and zip disks to back up a large amount of data that has been generated by an accounting firm.
wlad13 [49]

Answer:

D = 4, Z = 24

Step-by-step explanation:

6D+3Z = 96

5D+4Z = 116

multiply top by 5 and bottom by -6

top equation = 30D+15Z = 480

bottom equation = -30D-24Z = -696

Cancel 30D and -30 D

top equation  = 15Z = 480

Bottom equation = -24Z = -696

15Z - 24 Z = 480 - 696

-9Z = 216

Z = 216/9

Z = 24

Now that we have the value of Z, we can substitute it in any equation to find D

6D + 3(24) = 96

6D + 72 = 96

6D = 96 - 72

6D = 24

D = 24/6

D = 4

4 0
3 years ago
Guided Practice
irga5000 [103]
It’s choice A! :) y= -x - 6
3 0
2 years ago
Read 2 more answers
I need help. I suck at Geometry
Temka [501]

Answer:

25

Step-by-step explanation:

We can use the Pythagorean theorem to fin x

a^2 + b^2 = c^2  where a and b are the legs and c is the hypotenuse

7^2 + 24^2 = x^2

49+ 576 = x^2

625 = x^2

Take the square root of each side

sqrt( 625) = sqrt(x^2)

25 = x

4 0
3 years ago
Read 2 more answers
How do you find out if a decimal is terminating or repeating?
leva [86]

Answer:

A terminating decimal, terminates, or stops. For example: 1.5. A repeating decimal keeps repeating itself. For example: .999999999999 (and so on). Hope I helped!

Step-by-step explanation:

7 0
2 years ago
Other questions:
  • What is the volume of the pyramid
    8·1 answer
  • Which question can be represented by the equation? Times 1/8 equals three
    6·1 answer
  • All I need is the answer no explanation
    12·2 answers
  • PLEASE HELP I DON'T KNOW HOW TO DO THIS
    14·1 answer
  • Diagonalize a if possible. (find p and d such that a = pdp−1 for the given matrix
    7·1 answer
  • If a surface area of the Earth is about 196,9000,000 square miles, about how many square miles are covered in water
    8·1 answer
  • Please help me, Thank you
    7·1 answer
  • Find the value of x
    8·2 answers
  • Which fraction converts to a repeating decimal number?
    8·2 answers
  • What is the length of ac ?
    10·2 answers
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!